document.write( "Question 1017337: the sum of first two terms of a G P is x and the sum of last two terms is y. if there are nth terms in all find their common ratio \n" ); document.write( "

Algebra.Com's Answer #633638 by rothauserc(4718) $\"\"$ $\"About$

You can put this solution on YOUR website!
the nth term of a geometric sequence is defined
\n" ); document.write( ":
\n" ); document.write( "Xn = ar^(n-1) where a is the first term and r is the common ratio
\n" ); document.write( ":
\n" ); document.write( "we are given
\n" ); document.write( "X1 + X2 = x
\n" ); document.write( "a + ar = x
\n" ); document.write( "a = x / (r+1)
\n" ); document.write( ":
\n" ); document.write( "X(n-1) + Xn = y
\n" ); document.write( "ar^(n-2) + ar^(n-1) = y
\n" ); document.write( ":
\n" ); document.write( "now substitute for a
\n" ); document.write( ":
\n" ); document.write( "(x/(r+1))(r^(n-2) + (x/(r+1))(r^(n-1)) = y
\n" ); document.write( ":
\n" ); document.write( "xr^(n-2) + xr^(n-1) = y(r+1)
\n" ); document.write( ":
\n" ); document.write( "xr^(n-1)(r+1) = y(r+1)
\n" ); document.write( ":
\n" ); document.write( "xr^(n-1) = y
\n" ); document.write( ":
\n" ); document.write( "r^(n-1) = y / x
\n" ); document.write( ":
\n" ); document.write( "***********************
\n" ); document.write( "r = (y / x)^(1 / (n-1))
\n" ); document.write( "***********************\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );